Low Communication Self-stabilization through Randomization

Most self-stabilizing protocols rely on checking every neighbor of a node continuously to detect failures. Such protocols have a high communication cost, especially in dense graphs. Conceivably, one can check neighbors less often, reducing the amount of communication per round. However, delaying the checking delays the fault detection and the stabilization, and therefore has the potential of increasing the total amount of communication overhead until stabilization. In this paper, we strive to reduce "after stabilization" overhead, without increasing the "before stabilization" overhead. For that, we investigate the potential effect of randomization on the communication efficiency of self-stabilizing protocols. We present randomized low communication self-stabilizing algorithms for several major tasks, namely, spanning tree construction, distributed reset, and unison. We study this approach in a complete graph, since there the communication overhead of checking seems the highest when one strives for protocols that are also fast.

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